A289640 - OEIS

%I #25 Jul 11 2017 08:46:25

%S 24,393840,128962656,87898218720,42722691563664,23880530579622336,

%T 12556395110261366976,6777250576938845733312,

%U 3616836970791932655993144,1939629997080836352904793760,1037999388408269242271021494560

%N Coefficients in expansion of -q*E'_14/E_14 where E_14 is the Eisenstein Series (A058550).

%H Seiichi Manyama, <a href="/A289640/b289640.txt">Table of n, a(n) for n = 1..366</a>

%F a(n) = Sum_{d|n} d * A289029(d).

%F a(n) = 2*A288261(n)/3 + A288840(n)/2 + 28*A000203(n).

%F a(n) = -Sum_{k=1..n-1} A058550(k)*a(n-k) - A058550(n)*n.

%F G.f.: 2/3 * E_6/E_4 + 1/2 * E_8/E_6 - 7/6 * E_2.

%F a(n) ~ exp(2*Pi*n). - _Vaclav Kotesovec_, Jul 09 2017

%t nmax = 20; Rest[CoefficientList[Series[24*x*Sum[k*DivisorSigma[13, k]*x^(k-1), {k, 1, nmax}]/(1 - 24*Sum[DivisorSigma[13, k]*x^k, {k, 1, nmax}]), {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Jul 09 2017 *)

%Y -q*E'_k/E_k: A289635 (k=2), A289636 (k=4), A289637 (k=6), A289638 (k=8), A289639 (k=10), this sequence (k=14).

%Y Cf. A006352 (E_2), A058550 (E_14), A287964, A289029.

%K nonn

%O 1,1

%A _Seiichi Manyama_, Jul 09 2017